Chapter 14, Problem 28PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# The compound Xe(CF3)2 decomposes in a first-order reaction to elemental Xe with a half-life of 30. minutes. If you place 7.50 mg of Xe(CF3)2 in a flask, how long must you wait until only 0.25 mg of Xe(CF3)2 remains?

Interpretation Introduction

Interpretation: The time taken for the amount of Xe(CF3)2 has to be givem

Concept Introduction:

Integrated rate law for first order reaction:

Consider A as substance, that gives the product based on the equation,

aAproducts

Where a= stoichiometric co-efficient of reactant A.

Consider the reaction has first-order rate law,

Rate=-Δ[A]Δt=k[A]

The integrated rate law equation can be given as,

ln[A]t[A]o=-kt

The above expression is called integrated rate law for first order reaction.

Half life for first order reactions:

The half life for the first order reaction is constant and it is independent of the reactant concentration.

Half life period of first order reaction can be calculated using the equation,

t1/2=0.693k

Explanation

The time taken for the amount of SO2Cl2 is calculated as,

â€‚Â Reactionâ€‰rateÂ =Â kÂ [Xe(CF3)2]1.Given:t1/2â€‰=â€‰30Â mins;t1/2=0.693kk=0.69330Â mins=â€‰0.0231minâˆ’1[Xe(CF3)2]0â€‰â€‰=â€‰â€‰7.50mg[Xe(CF3)2]t=0.25â€‰mgTherefore,FirstÂ orderÂ rateÂ law,ln[Xe(CF3)2]tâ€‰=â€‰-â€‰kâ€‰tÂ +Â ln[Xe(CF3)2]0ln[0

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